Hi Martin, Thanks a lot for the elucidation! I found out after your answer that there is already an AnisotropicPolynomials class. It was remiss of me not even doing a quick search...
I noticed that FE_DGQ class is derived from FE_Poly with a polynomial space argument: *TensorProductPolynomials <https://dealii.org/current/doxygen/deal.II/classTensorProductPolynomials.html><dim>(Polynomials <https://dealii.org/current/doxygen/deal.II/namespacePolynomials.html>::generate_complete_Lagrange_basis(internal <https://dealii.org/current/doxygen/deal.II/namespaceinternal.html>::FE_DGQ <https://dealii.org/current/doxygen/deal.II/classFE__DGQ.html>::get_QGaussLobatto_points(degree))* It seems that if we write a FE_DGQAnistropic class, we'd probably want to replace this argument with a counterpart of the AnisotropicPolynomials class. Do you think this replacement alone would cut it? We are not looking for any more features out of the fe space than what FE_DGQ is already doing. FE_DGQ involves implementing quite a bunch of virtual functions <https://dealii.org/current/doxygen/deal.II/fe__dgq_8h_source.html#l00375>. Apart from, as far as I can parse, FE_DGQ<dim, spacedim>::rotate_indices <https://dealii.org/current/doxygen/deal.II/classFE__DGQ.html#ab7491f8ec8f7081f1f989f1e3e5da5f7>, they seem to be coordinate direction agnostic. Would really appreciate if you can shed more light on this! Best, Greg On Sunday, March 12, 2023 at 8:33:02 AM UTC Martin Kronbichler wrote: > Dear Greg, > > Just to extend on what Peter said: It should be possible to define > anisotropic degrees in a completely discontinuous finite element, say > FE_DGP or FE_DGQ. In that case, you would derive from `FE_Poly` and insert > an anisotropic polynomial space, doing whatever you think is appropriate. > For elements imposing some continuity, include FE_FaceP/FE_FaceQ or the > regular H1 functions (FE_Q), you can't do that as Peter said. However, one > could work around this by constructing constraints that constrain the > polynomial space of uniform high order in one of the directions to the > lower polynomial degree. It would be a bit of work to realize this (say > 200-400 lines of code to set up the constraints), but the easiest solution > I could come up. > > Best, > Martin > > > On 11.03.23 17:26, Greg Wang wrote: > > Hi Peter, > > Thanks a lot for the info! > > We have recently implemented in deal.II a space-time HDG method for the > advection-diffusion problem on deforming domains. Our analysis allows the > spatial polynomial order p_s to differ from the temporal one p_t. When p_t > = p_s, we just call FE_DGP, FE_FaceP constructors with nothing extra to do > and the rates come out nicely matching the a priori rates of convergence. > And now we are trying to have a p_t = p_s +1 test case to further validate > our analysis, which led to this post. > > Best regards, > Greg > > On Saturday, March 11, 2023 at 2:20:37 PM UTC peterr...@gmail.com wrote: > >> Hi Greg, >> >> unfortunately we do not support anisotropic polynomials: we make the >> assumption that all faces (of the same type) and lines have the same number >> of DoFs. For what do you need such polynomial spaces? >> >> Best, >> Peter >> >> On Saturday, 11 March 2023 at 15:05:25 UTC+1 ygre...@gmail.com wrote: >> >>> Hi there, >>> >>> I was wondering if finite elements with anisotropic polynomial degrees >>> are possible in deal.II. As an example, for a 3D element, can we construct >>> a tensor product polynomial space of {1,x,y,z,xy,xz,yz, z^2,xz^2,yz^2}, >>> i.e., order 1 in x- and y-directions and 2 in z-direction? >>> >>> I was looking at, for example, constructors of FE_DGQ() class [1]. The >>> second constructor [2] takes an arbitrary vector of polynomials to build >>> the tensor product polynomial space. This is close to what I want but it >>> seems the argument can only be one-dimensional polynomials, which means >>> equal order on all dimensions. >>> >>> Would really appreciate any insights and/or tips! >>> >>> Best, >>> Greg >>> >>> ------------------------------------------ >>> [1] https://dealii.org/current/doxygen/deal.II/classFE__DGQ.html >>> [1] >>> https://dealii.org/current/doxygen/deal.II/fe__dgq_8cc_source.html#l00100 >>> >> -- > The deal.II project is located at http://www.dealii.org/ > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > --- > You received this message because you are subscribed to the Google Groups > "deal.II User Group" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to dealii+un...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/3dcc5829-7218-4c51-9c86-ae8fccb4ba82n%40googlegroups.com > > <https://groups.google.com/d/msgid/dealii/3dcc5829-7218-4c51-9c86-ae8fccb4ba82n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. 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